Bond strength uncertainty quantification via confidence intervals for nondestructive evaluation of bonded composites

As bonded composite materials are used more frequently for aerospace applications, it is necessary to certify that parts achieve desired levels of certain physical characteristics (e.g., strength) for safety and performance. Nondestructive evaluation (NDE) of adhesively bonded structures enables verification of bond physical characteristics, but uncertainty quantification (UQ) of NDE estimates is crucial for understanding risks, especially for NDE estimates like bond strength. To address the critical need for NDE UQ for adhesive bond strength estimates, we propose an optimization--based approach to computing finite--sample confidence intervals showing the range of bond strengths that could feasibly be produced by the observed data. A statistical inverse model approach is used to compute a confidence interval of specimen interfacial stiffness from swept--frequency ultrasonic phase observations and a method for propagating the interval to bond strength via a known interfacial stiffness regression is proposed. This approach requires innovating the optimization--based confidence interval to handle both a nonlinear forward model and unknown variance and developing a calibration approach to ensure that the final bond strength interval achieves at least the desired coverage level. Using model assumptions in line with current literature, we demonstrate our approach on simulated measurement data using a variety of low to high noise settings under two prototypical parameter settings. Relative to a baseline approach, we show that our method achieves better coverage and smaller intervals in high--noise settings and when a nuisance parameter is near the constraint boundary.